Revista Matemática Iberoamericana


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Volume 32, Issue 4, 2016, pp. 1277–1294
DOI: 10.4171/RMI/916

Published online: 2016-12-16

On the $\ell^s$-boundedness of a family of integral operators

Chiara Gallarati[1], Emiel Lorist[2] and Mark Veraar[3]

(1) Delft University of Technology, Netherlands
(2) Delft University of Technology, Netherlands
(3) Delft University of Technology, Netherlands

In this paper we prove an $\ell^s$-boundedness result for integral operators with operator-valued kernels. The proofs are based on extrapolation techniques with weights due to Rubio de Francia. The results will be applied by the first and third author in a subsequent paper where a new approach to maximal $L^p$-regularity for parabolic problems with time-dependent generator is developed.

Keywords: $\ell^s$-boundedness, extrapolation, integral operators, $A_p$-weights, Hardy–Littlewood maximal function

Gallarati Chiara, Lorist Emiel, Veraar Mark: On the $\ell^s$-boundedness of a family of integral operators. Rev. Mat. Iberoamericana 32 (2016), 1277-1294. doi: 10.4171/RMI/916